scholarly journals The Natural Gas Cash-Out Problem: A Bilevel Optimal Control Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Vyacheslav V. Kalashnikov ◽  
Francisco Benita ◽  
Patrick Mehlitz
Keyword(s):  
Optimal Control ◽  
Natural Gas ◽  
Mixed Integer ◽  
Integer Programming Problem ◽  
Control Approach ◽  
Finite Dimensional ◽  
Upper Level ◽  
Pure State Constraints ◽  
Mixed Integer Programming Problem ◽  
Theoretical Results

The aim of this paper is threefold: first, it formulates the natural gas cash-out problem as a bilevel optimal control problem (BOCP); second, it provides interesting theoretical results about Pontryagin-type optimality conditions for a general BOCP where the upper level boasts a Mayer-type cost function and pure state constraints, while the lower level is a finite-dimensional mixed-integer programming problem with exactly one binary variable; and third, it applies these theoretical results in order to find possible local minimizers of the natural gas cash-out problem.

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

scholarly journals A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Godfrey Chagwiza ◽  
Chipo Chivuraise ◽  
Christopher T. Gadzirayi
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Moringa Oleifera ◽  
Bat Algorithm ◽  
Mixed Integer ◽  
Poultry Feed ◽  
Integer Programming Problem ◽  
Optimum Solution ◽  
Mixed Integer Programming Problem ◽  
Number Of Iterations

In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.

Scheduling of Yard Truck Considering Loading and Unloading Simultaneously in an Underground Container Logistics System

2021 ◽  
pp. 036119812110478
Author(s):  
Yinping Gao ◽  
Daofang Chang ◽  
Jun Yuan ◽  
Chengji Liang
Keyword(s):  
Genetic Algorithm ◽  
Container Terminals ◽  
Mixed Integer ◽  
Operating Efficiency ◽  
Adaptive Genetic Algorithm ◽  
Integer Programming Problem ◽  
Logistics System ◽  
Container Logistics ◽  
Loading And Unloading ◽  
Mixed Integer Programming Problem

With the rapid growth of containers and scarce of land, the underground container logistics system (UCLS) presents a logical alternative for container terminals to better protect the environment and relieve traffic pressure. The operating efficiency of container terminals is one of the competitive edges over other terminals, which requires UCLS to be well integrated with the handling process of the storage yard. In UCLS, yard trucks (YTs) serve different handling points dynamically instead of one fixed handling point, and yard cranes (YCs) perform loading and unloading simultaneously. To minimize the total time of handling all containers in UCLS, the mixed integer programming problem is described and solved using an adaptive genetic algorithm (AGA). The convergence speed and accuracy of AGA are demonstrated by comparison with conventional genetic algorithm (GA). Additionally, AGA and CPLEX are compared with different scale cases. Experimental results show that the proposed algorithm is superior to CPLEX in resulted solutions and calculation time. A sensitivity analysis is provided to obtain reasonable numbers of YTs for scheduling between handling points and the storage yard in UCLS.

The Optimal Controlled Partitioning Strategy for Power System Based on Master-Slave Problem

2013 ◽  
Vol 385-386 ◽  
pp. 999-1006
Author(s):  
Wei Wang ◽  
Ting Yu ◽  
Tian Jiao Pu ◽  
Ai Zhong Tian ◽  
Ji Keng Lin
Keyword(s):  
Large Scale ◽  
Optimization Method ◽  
Mixed Integer ◽  
Master Problem ◽  
Decomposition Algorithms ◽  
Integer Programming Problem ◽  
Complete Model ◽  
New Approach ◽  
Mixed Integer Programming Problem ◽  
Partitioning Strategy

Controlled partitioning strategy is one of the effective measures taken for the situation when system out-of-step occurs. The complete splitting model, mostly solved by approximate decomposition algorithms, is a large-scale nonlinear mixed integer programming problem. A new alternate optimization method based on master-slave problem to search for optimal splitting strategy is proposed hereby. The complete model was converted into master-slave problems based on CGKP (Connected Graph Constrained Knapsack Problem). The coupling between master problem and slave problem is achieved through load adjustment. A better splitting strategy can be obtained through the alternating iteration between the master problem and the salve problem. The results of the examples show that the method can obtain better splitting strategy with less shed load than other approximate algorithms, which verifies the feasibility and effectiveness of the new approach presented.

scholarly journals Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

2013 ◽  
Vol 36 (5) ◽  
pp. 1267-1277 ◽  
Author(s):  
Pierre Bonami ◽  
Alberto Olivares ◽  
Manuel Soler ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Trajectory Optimization ◽  
Mixed Integer ◽  
Control Approach ◽  
Aircraft Trajectory ◽  
Optimal Control Approach
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